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Here is a quick guide to doing problems involving spring potential energy, to help you do your physics homework or assignment:
The potential energy contained in a spring is:
Example
1. A 0.250-kg block is placed on a light vertical spring (k = 5.00 x 103 N/m) and pushed downwards, compressing the spring 0.100 m. After the block is released, it leaves the spring and continues to travel upwards. What height above the point of release will the block reach if air resistance is negligible?
Solution
The potential energy of the spring at its lowest point, is turned into gravitational potential energy at it's highest point. Therefore,
(0.100 \, m)}{2(9.8 \, m/s^2)(0.250 \, kg)} = 102 \, meters "\frac{1}{2}k x^2 = mgh \,\,\, \to \,\,\, h=\frac{k x^2}{2gm} = \frac{(5.00 \times 10^3 \, N/m)(0.100 \, m)}{2(9.8 \, m/s^2)(0.250 \, kg)} = 102 \, meters")
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